Foundation Check In - 10.01 Units and
measurement
1. The maximum speed on UK roads is 70 mph.
Convert this speed into km/h using 1 mile  1.6 km.
2. Convert a density of 2.5 kg/m3 into g/cm3.
3. An average speed is given as
3x
km/h. What is this in m/s?
5
4. This is the formula for pressure.
Pressure 
Force
Area
A cuboid with a base area of 85 cm2 applies a force of 170 N to the floor. What is the
pressure that the floor is under in N/cm2?
5. The density of the air around us is 1.3 kg/m3. What is the volume of a balloon that can
hold 4.55 g of air?
6. A map has a scale of 1 : 25 000, and a road marked on this map is 7 cm long. The
same road is marked on a different map and measures 3.5 cm long. Explain how you
could use this information to work out the scale on the second map.
7. Platinum has a density of 21.4 g/cm3 and silver has a density of 10.5 g/cm3.
Without calculating their weights explain which is heavier, 50 cm3 of platinum or 100
cm3 of silver.
8. It takes a snail one week to travel 1 kilometre. Calculate the approximate speed at
which the snail is travelling and justify your choice of units.
9. A cuboid block of concrete applies a force of 4500 N to a table so the pressure exerted
on the table is 90 N/cm2. One side of the base of the cuboid block is 5 cm. What is the
length of the other side of the base? (Note: you may use the formula provided in
question 4)
10. A map has a scale of 1 : 10 000. On the map, a post office is directly north of a school
and a museum is directly east of the same school. The buildings are linked by three
straight roads. Ahmed measures these roads on his map. The distance between the
post office and the museum is 15 cm, and the distance between the post office and the
school is 9 cm. How far is it from the school to the museum in kilometres?
Extension
A crane needs to lift a steel joist.
The joist is a cuboid with dimensions 2.5 m by 0.2 m by 0.2 m.
Steel has a density of 8.05 g/cm3.
The crane can lift a maximum load of 1.5 tonnes.
Can the crane be used to lift the joist? Show your working.
Answers
1. 112 km/h
2. 0.0025 g/cm3
3.
x
m/s
6
4. 2 N/cm2
5. 0.0035 m3
6. The road is half as long on the new map so the scale must be double, or 1 : 50 000
7. The platinum is heavier; it has half the volume, but more than double the density.
8. 0.165 cm/s or 9.92 cm/min. The most commonly used unit for speed, km/h, would be
too large a unit for the answer to be meaningful; even m/s is slightly too large for the
numerical values given.
9. 10 cm
10. 1.2 km
Extension
Volume of joist  0.2  0.2  2.5  0.1 m3
Mass of joist  density  volume; density is g/cm3 so need to convert to kg/m3, 8.05 g/cm3
 8050 kg/m3
Mass of joist  8050  0.1  805 kg
1.5 tonne  1500 kg
Yes, the crane can lift the joist.
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Assessment
Objective
Qu.
Topic
R
A
G
Assessment
Objective
Qu.
Topic
AO1
1
Convert simple compound units (speed)
AO1
1
Convert simple compound units (speed)
AO1
2
Convert other compound units (density)
AO1
2
Convert other compound units (density)
AO1
3
Convert compound units in an algebraic context (speed)
AO1
3
Convert compound units in an algebraic context (speed)
AO1
4
Use compound units
AO1
4
Use compound units
AO1
5
Know and apply density  mass ÷ volume
AO1
5
Know and apply density  mass ÷ volume
AO2
6
Use the scale of a map
AO2
6
Use the scale of a map
AO2
7
Apply knowledge of density  mass ÷ volume
AO2
7
Apply knowledge of density  mass ÷ volume
AO2
8
Use and convert standard units or simple compound units
(speed)
AO2
8
Use and convert standard units or simple compound units
(speed)
AO3
9
Solve a problem using density  mass ÷ volume
AO3
9
Solve a problem using density  mass ÷ volume
AO3
10
Use the scale of a map to solve a problem
AO3
10
Use the scale of a map to solve a problem
Assessment
Qu.
Assessment
Qu.
Objective
Topic
R
A
G
Objective
Topic
AO1
1
Convert simple compound units (speed)
AO1
1
Convert simple compound units (speed)
AO1
2
Convert other compound units (density)
AO1
2
Convert other compound units (density)
AO1
3
Convert compound units in an algebraic context (speed)
AO1
3
Convert compound units in an algebraic context (speed)
AO1
4
Use compound units
AO1
4
Use compound units
AO1
5
Know and apply density  mass ÷ volume
AO1
5
Know and apply density  mass ÷ volume
AO2
6
Use the scale of a map
AO2
6
Use the scale of a map
AO2
7
Apply knowledge of density  mass ÷ volume
AO2
7
Apply knowledge of density  mass ÷ volume
AO2
8
Use and convert standard units or simple compound units
(speed)
AO2
8
Use and convert standard units or simple compound units
(speed)
AO3
9
Solve a problem using density  mass ÷ volume
AO3
9
Solve a problem using density  mass ÷ volume
AO3
10
Use the scale of a map to solve a problem
AO3
10
Use the scale of a map to solve a problem
R
A
G
R
A
G